#include <algorithm>
#include <vector>
using namespace std;
/*
 * @lc app=leetcode.cn id=343 lang=cpp
 *
 * [343] 整数拆分
 */

// @lc code=start
class Solution {
public:
    int integerBreak(int n) {
        vector<int> dp(n + 1, 0);
        dp[0] = 0; dp[1] = 0; dp[2] = 1;
        for (int i = 3; i <= n; i++) {
            for (int j = 1; j <= i - j; j++) {
                dp[i] = max(dp[i], max(dp[j] * dp[i - j], max(j * dp[i - j], dp[j] * (i - j))));
                dp[i] = max(dp[i], j * (i - j));
            }
        }
        return dp[n];
    }
};
// @lc code=end

